Subgroups — C₃×C₄×Q₁₆ #5313

Order 192.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×Q₈	C₂	1	2	yes	maximal
3	C₃×#107	C₂	1	1	yes	maximal, characteristic
4	C₃×#103	C₂	1	2	yes	maximal
5	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
6	C₄×Q₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	C₂²	1	2	yes	—
8	C₃×Q₁₆	C₄	1	4	yes	direct product factor
9	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
11	C₃×C₄⋊C₄	—	2	2	no	—
12	C₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₃×C₄²	—	2	2	no	—
14	C₃×C₄²	C₂²	1	1	yes	characteristic
15	C₂×Q₁₆	C₂×C₃	1	1	yes	characteristic
16	C₄×Q₈	C₂×C₃	1	2	yes	—
17	#107	C₂×C₃	1	1	yes	characteristic
18	#103	C₂×C₃	1	2	yes	—
19	C₄×C₈	C₂×C₃	1	1	yes	characteristic
20	C₃×Q₈	—	2	2	no	—
21	C₃×Q₈	C₂×C₄	1	4	yes	—
22	C₂×C₃×C₄	—	2	2	no	—
23	C₂×C₃×C₄	—	2	2	no	—
24	C₂×C₃×C₄	D₄	1	1	yes	characteristic
25	C₂×C₃×C₄	D₄	1	1	yes	characteristic
26	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
27	C₃×C₈	—	2	1	no	—
28	C₃×C₈	C₂×C₄	1	2	yes	—
29	C₂×Q₈	C₂²×C₃	1	2	yes	—
30	Q₁₆	C₃×C₄	1	4	yes	direct product factor
31	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
32	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
33	C₄⋊C₄	—	2	2	no	—
34	C₄⋊C₄	C₂²×C₃	1	2	yes	—
35	C₄²	—	2	2	no	—
36	C₄²	C₂²×C₃	1	1	yes	characteristic
37	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
38	C₃×C₄	—	2	4	no	—
39	C₃×C₄	—	2	1	no	—
40	C₃×C₄	—	4	2	no	—
41	C₃×C₄	Q₁₆	1	2	yes	direct product factor
42	C₃×C₄	C₂²×C₄	1	1	yes	characteristic
43	C₃×C₄	#41	1	1	yes	characteristic
44	Q₈	—	2	2	no	—
45	Q₈	C₂×C₃×C₄	1	4	yes	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	C₃×D₄	1	1	yes	characteristic
49	C₂×C₄	C₃×D₄	1	1	yes	characteristic
50	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
51	C₈	—	2	1	no	—
52	C₈	C₂×C₃×C₄	1	2	yes	—
53	C₂×C₃	C₄×D₄	1	1	yes	characteristic
54	C₂×C₃	C₂×Q₁₆	1	1	yes	characteristic
55	C₂×C₃	#135	1	1	yes	characteristic
56	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
57	C₄	—	2	4	no	—
58	C₄	—	2	1	no	—
59	C₄	—	4	2	no	—
60	C₄	C₃×Q₁₆	1	2	yes	direct product factor
61	C₄	C₂²×C₃×C₄	1	1	yes	characteristic
62	C₄	C₃×#41	1	1	yes	characteristic
63	C₃	C₄×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
64	C₂	C₃×C₄×D₄	1	1	yes	characteristic
65	C₂	C₂×C₃×Q₁₆	1	1	yes	characteristic
66	C₂	C₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₄
commutator	C₄	C₂²×C₃×C₄
Frattini, cosocle	C₂×C₄	C₂³×C₃
socle, prime radical	C₂²×C₃	C₂×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄² ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
6. C₄×Q₁₆	C₃	direct (N × H)
8. C₃×Q₁₆	C₄	direct (N × H)
30. Q₁₆	C₃×C₄	direct (N × H)
41. C₃×C₄	Q₁₆	direct (N × H)
60. C₄	C₃×Q₁₆	direct (N × H)
63. C₃	C₄×Q₁₆	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×Q₁₆	2
C₃×C₄×Q₈	2
C₃×#107	2
C₃×#103	2
C₃×C₄×C₈	2
C₄×Q₁₆	3

Subgroups — C3×C4×Q16 #5313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×Q₁₆ #5313